aa r X i v : . [ a s t r o - ph ] J un **FULL TITLE**ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION****NAMES OF EDITORS** Star Formation in Molecular Clouds?
Neal J. Evans II
The University of Texas at Austin, Department of Astronomy, 1University Station, C1400, Austin, TX 78712-0259, USA
Abstract.
Using studies of nearby star formation with Spitzer, I will arguethat star formation is restricted to dense cores within molecular clouds. Thenature of these dense cores and their connection to star formation will be dis-cussed. Their distribution over masses and over the cloud is similar to thatof stars, and their efficiency of forming stars is much higher than that of thewhole cloud. Moving to regions forming more massive stars, we find that themass distribution of the dense clumps is similar to that of OB associations. Theinfrared luminosity per unit mass of dense gas is high and comparable to thatseen in starburst galaxies. The relation between star formation and dense gasappears to be linear. Understanding the Kennicutt-Schmidt law requires an un-derstanding of what controls the conversion of gas into the dense entities wherestars actually form.
1. Introduction
The image that comes to mind when we talk about star formation across disci-plinary lines is that of the “sight-challenged” villagers and the elephant. Eachfeels a different part of the elephant and comes to different conclusions aboutwhat it is. Discussions of star formation within the Milky Way use languageunfamiliar to those who work on star formation in other galaxies and vice versa.If we are to progress, we need to find a common language.Studies of low mass star formation in nearby (typically within 500 pc) cloudscan speak in detail about the distribution of star formation, the timescales forvarious phases, and the current efficiency in stellar mass per cloud mass. De-tailed, predictive theoretical models exist for the formation of individual stars(e.g., Shu et al. 1987). There is a strong focus on detailed studies of the flow ofmaterial from envelope to disk to star and on the connection to planet formation(e.g., many articles in Reipurth et al. 2007). We can also provide observationalconstraints on the origin of the initial mass function. However, these studies arenot directly relevant to star formation on galactic scales because low-mass starformation is not observable at large distances.Regions forming more massive stars begin to show up at about 440 pc(Hirota et al. 2007) in the Orion complex but most lie at distances of kpc, withthe most impressive being in the Galactic ring, located about 5 kpc from thecenter of the Milky Way (Clemens et al. 1988). For the most part, we are reallytalking about formation of clusters of stars, including both high and low massstars, though most forming clusters do not survive (Lada & Lada 2003). Ourknowledge of these regions is much less detailed, owing to the lack of spatial1
Evans, N. resolution, and theoretical predictions are less well developed. Considerabletheoretical progress is being made, but there are fundamental disagreements onsome issues (cf. Krumholz et al. 2005, Bonnell & Bate 2006, Martel et al. 2006).For most of the distant regions, we do not separate individual stars, but ratherwe characterize the star formation in terms of surrogates, such as the far-infraredluminosity ( L IR ) and the mass of molecular material. While less detailed, thesecrude measures are more compatible with what can be done in other galaxies.Discussion of star formation in other galaxies speaks nearly exclusively interms of “Schmidt Laws”. The original version compared the scale heights ofyoung stars and the HI gas and concluded that the star formation rate is pro-portional to the square of the volume density (Schmidt 1959). Were this to bedone today, recognizing that star formation is restricted to molecular gas, onewould probably infer a linear relationship. However, surface density is moreamenable to study in other galaxies and modern versions find relations betweenthe surface densities of star formation and gas (Kennicutt 1998). A power lawabove a threshold provides a remarkably good fit:Σ( SF )(M ⊙ yr − kpc − ) = (2 . ± . × − (Σ( gas ) / ⊙ pc − ) . ± . over a wide range of galaxy types and star formation rates. Several explana-tions have been offered for the value of the exponent (Elmegreen & Scalo 2004,Krumholz & McKee 2005, Shu et al. 2007). Models of galaxy formation andevolution generally use a Kennicutt-Schmidt relation to simulate star forma-tion, which is treated as “sub-grid physics.”To return to the elephant analogy, each villager feels a different part of theelephant, but also speaks a different language, which is only partly understood,and often misinterpreted, by the others. But the need for communication isgreat as rapid progress is occurring in studies of massive star formation in ourgalaxy. At the same time, studies of galaxy formation are progressing rapidly,including both archaeological studies of the oldest stars and direct look-backstudies of high-z luminous starbursts. Can we find a common language?I will summarize recent progress in studies of both local, low-mass andclustered, high-mass star formation in our Galaxy, and then I will discuss someconnections that can be made.
2. Low-mass Star Formation in Nearby Clouds
For convenience, I will focus here on recent results from the
Spitzer legacyproject, “From Molecular Cores to Planet-Forming Disks”, known as “Coresto Disks” or c2d (Evans 2003). In particular, I will concentrate on studies offive large nearby clouds. For three of these clouds (Perseus, Serpens, and Ophi-uchus), we have complementary information on the dust emission at 1 mm usingBolocam (Enoch et al. 2006, Young et al. 2006, Enoch et al. 2007) and molec-ular line emission (Ridge et al. 2006). These studies provide the first completecoverage of molecular clouds in tracers of gas, dense cores, and young stellar (orsubstellar) objects (YSOs) down to luminosities of about 0.01 L ⊙ .Comparison of the CO and CO maps with the Bolocam maps shows thatthe dense ( n > × cm − ) cores traced by dust continuum emission at mil-limeter wavelengths are distributed very non-uniformly over the cloud. Dense tar Formation in Molecular Clouds? CO. Thedense cores strongly prefer regions of high overall extinction, with 75% of densecores found within extinction contours that contain only 0.1 to 0.3 of the totalcloud mass (Enoch et al. 2007). Comparison of the dense core distribution tothat of YSOs shows a strong correlation, especially for the early stages of starformation. The dense cores are clearly the sites of star formation; most of thecloud is completely inactive.Until spectral types are available for more of the YSOs, we cannot constructIMFs for the clouds, but all data so far are consistent with a typical IMF.The core mass distribution for starless cores, averaging over all 3 clouds, isremarkably consistent with the usual IMF, but shifted to larger masses by afactor <
4, suggesting that the IMF is set by the core mass distribution withan efficiency >
25% (Enoch et al. in prep.). Similar conclusions have beenreached by Alves et al. (2007) using extinction mapping to trace cores; theirmethod produces less uncertain masses but probes lower densities on average.Of course, the similarity of the IMF and the core mass distribution could befortuitous if cores of different masses have different lifetimes (Clark et al. 2007).We define the actual efficiency of star formation as the fraction of the massthat ends up in stars (or substellar objects): ǫ ⋆ = M ⋆ / ( M ⋆ + M gas ) ≈ M ⋆ /M gas . The final efficiency, after the gas is consumed or dissipated, is impossible todetermine directly since the gas lifetime vastly exceeds human lifetimes, butwe can constrain it. In practice we measure the current efficiency using thecurrent mass in stars and in gas. To get a star formation rate ( ˙ M ⋆ ), we assumea mean stellar mass of 0.5 M ⊙ (consistent with actual determinations in onecloud, Alcal`a et al. in prep.), and a timescale of 2 Myr (essentially the half-lifeof infrared excesses that the c2d observations are sensitive to). It is possiblefor these nearby regions to separate the efficiency, as defined above, from thequestion of the speed of star formation. We define the timescale for gas depletion,as in extragalactic studies: t dep = M ( gas ) / ˙ M ⋆ , and the speed is 1 /t dep . Krumholz & Tan (2007) define the speed as SF R ff = t ff /t dep = ˙ M ⋆ t ff /M ( gas ) . This is the speed (1 /t dep ) normalized to the maximum likely speed (1 /t ff ), orthe star formation rate normalized to the maximum possible in a free fall time.The preliminary results for these quantities for the five large clouds studiedby c2d are summarized here. The total mass in YSOs is about 2% to 4% ofthe cloud mass (e.g., Harvey et al. 2007, Evans et al. in prep.) consistent withearlier conclusions that star formation is inefficient. The total mass in densecores is only 1% to 4% of the total cloud mass included in the A V = 2 contour.Low star formation efficiency begins with inefficient core formation. The valuesof ˙ M ⋆ range from 6.0 to 71 M ⊙ /Myr, a significant range. Star formation is slow:the depletion timescales for the whole molecular clouds are t dep = 50–90 Myr,much longer than most estimates of cloud lifetimes of 5–10 Myr. While further Evans, N. star formation is likely, the final efficiencies are likely to remain low. In contrast,the depletion times for dense cores, the actual sites of star formation, are 0.6–3.5 Myr, and masses in dense cores are similar to current masses in YSOs. Starformation is fast and efficient in dense gas .What about the speed relative to that obtained from assuming free fall? Incalculating
SF R ff , we use the mean density of the relevant unit to calculate thefree fall time. The SF R ff is 0.02 to 0.03 for the cloud as a whole, consistentwith long-standing arguments against efficient star formation at the free-fallrate (e.g., Zuckerman & Evans 1974). Considering the clump that is forming acluster, the SF R ff increases to 0.1 to 0.3, but if we use the mean density of anindividual dense core, the SF R ff is only 0.03 to 0.12. Star formation remains“slow” compared to a free fall time. This slowness cannot be blamed entirely ona slow prestellar phase; comparison of the numbers of dense, starless (prestellar)cores to the numbers of protostellar cores yields lifetimes of a few free-fall timesonce the density exceeds about 2 × cm − (Enoch et al. in prep).Does the surface density relation (Kennicutt 1998) have any relevance tolocal star formation? This one is hard to test locally because of incompleteness,but we can make a rough estimate. With a local gas surface density of 6.5 M ⊙ pc − (L. Blitz, pers. comm.), of which about 85% is HI (Levine et al. 2006,Dame 1993), the Kennicutt relation would predict Σ( SF ) = 3 . × − M ⊙ yr − kpc − . Lada & Lada (2003) estimate that embedded clusters contribute,to within a factor of 3, Σ( SF ) = 3 × − M ⊙ yr − kpc − within a radius of 0.5kpc. This is surely an underestimate until we have a more complete census of allclouds within the local area, but it is already remarkably close to the prediction.A more extensive study of this topic can be found in Blitz & Rosolowsky (2006).It is interesting to note that the low-mass star formation in the clouds studied bythe c2d project would not be apparent to the usual tracers used in extragalacticstudies, with the possible exception of L IR .The lessons we should take from these very detailed studies of nearby cloudsare as follows. The fundamental units of star formation are dense cores, notmolecular clouds, per se (hence the question mark in the title). The cores arenot located randomly over cloud faces, but are concentrated in clumps, whichare forming clusters, and filaments, which tend to form smaller aggregates. Thecore mass distribution may determine the IMF. Star formation in molecularclouds is very inefficient (2–4%), but quite efficient in dense cores ( >
3. Massive, Clustered Star Formation
With the exception of a few, relatively nearby regions of massive, clustered starformation, such as the Orion region (e.g., Hillenbrand 1997, Lada & Lada 2003,Allen et al. 2007), we do not have such detailed information on stellar IMF, ages,efficiencies, etc. Instead we accept cruder measures, but these provide a bridgeto star formation in other galaxies. Theories are not well developed yet, butprogress is being made, as discussed at the meeting by Bonnell, Dobbs, andKrumholz. tar Formation in Molecular Clouds?
IRAS sources (Sridharan et al. 2002; Beuther et al. 2002). An unbiasedsurvey of 1 mm continuum emission now underway using Bolocam will provide amore complete census (Williams et al. 2007) and deeper surveys with SCUBA-2and far-infrared surveys with Herschel will follow. We should soon have a muchmore complete picture of star formation sites in the Milky Way.For now, I will focus on results from the survey toward water masers(Plume et al. 1992), which has been followed up by many other studies obtain-ing gas densities from multitransition CS observations (Plume et al. 1997), im-ages of dust emission at 350 µ m (Mueller et al. 2002), maps of CS J = 5 − clumps . The dense clumps are the sites of cluster formation and we reserve theterm core to refer to the structure that forms one or a few stars.The dense clumps can be fitted to power law density profiles with exponentsvery similar to those of dense cores forming low mass stars, but the density,measured at the same radius is typically 100 times higher and the linewidthsare typically 16 times wider. Some show evidence in the line profiles for inwardmotions (Wu & Evans 2003), similar to those seen in some low mass cores.In general, they are scaled up versions of low-mass dense cores. This point isimportant, as some authors use “clump” to mean something less dense than acore. Massive, dense clumps are denser than the low mass cores. The clumpswithin them are presumably even denser, but they have been hard to separatecleanly.The mass function of the dense clumps is steeper that that of molecularclouds or of less dense clumps traced by CO isotopes (Shirley et al. 2003),but it is incomplete below about 1000 M ⊙ . Above that level, it is similar tothe distribution of the total masses of OB associations (Massey et al. 1995;McKee & Williams 1997). These dense clumps are very likely to be the siteswhere clusters and OB associations form. However, it has been difficult tostudy the forming stars themselves because of the heavy extinction and largedistances. The GLIMPSE legacy project (Benjamin et al. 2003) using the IRACinstrument on Spitzer is revealing clusters in some of these, but the strong diffuseemission in the IRAC bands makes it difficult to extract detailed information onthe stellar content (Nordhaus et al. in prep).Our observational measures are the luminosity in a molecular line or indust continuum at long wavelengths, which are tracers of the mass of dense gas,and the bolometric luminosity measured by integrating over the full spectrum ofdust emission. The line luminosities of tracers of dense gas, in particular CS andHCN, trace very well the virial mass of dense gas (e.g., Wu et al. in prep.). Theintegrated infrared luminosity ( L IR ) traces the star formation rate ( ˙ M ⋆ ) givenenough time for the IMF to be reasonably sampled (Krumholz & Tan 2007).Both these measures are subject to fluctuations about mean values of at least afactor of 3. Despite the variations, L IR correlates well with L Mol or M vir .Without a detailed census of the stellar content, we cannot compute thestar formation efficiency in the same sense ( ǫ ⋆ ) as we could for low mass star Evans, N. formation, but the similarity of the mass function to that of OB associationssuggests reasonably high efficiency in the dense gas.We will use an efficiency measure common in the extragalactic context asthe star formation rate per unit mass of gas (“ ǫ ” = ˙ M ⋆ /M ( gas ). Note thatthis “efficiency” is really the speed (1 /t dep ) unnormalized to the free fall time.In observational terms, this is measured by L IR /L Mol . As for low mass starformation, the “ ǫ ” is very low for molecular clouds as a whole, but much higherfor dense gas (e.g., a factor of 30 higher in one study, Mueller et al. 2002).Krumholz & Tan (2007) have argued that star formation is also slow relative toa free-fall time ( SF R ff ), though again there is some evidence that SF R ff ishigher in the densest gas, probed for example by the CS J = 5 −
4. Star Formation in Galaxies
Since we seek a connection between studies of star formation in our Galaxy andextragalactic star formation, we will focus on studies using common tracers.In dusty galaxies, the star formation rate is traced by L IR . This is basicallya calorimetric method: the dust absorbs all the energy from young stars andre-radiates in the infrared. The advantage is that there is no need for uncertainextinction corrections, which are needed for ultraviolet or H α measures of starformation. However, one is assuming that all the light is indeed absorbed, sosome star formation can be missed (this problem can apparently be alleviatedby combining infrared and H α observations, as described by Calzetti at thismeeting). Also, a calorimeter measures any heat input, so heating by older starsor an AGN can confuse matters. In practice, this method is applied only to sys-tems where star formation overwhelms the heating by older stars. Assessing thecontribution of AGNs can be trickier, especially for high-z systems. A commoncalibration, based on a continuous burst model is that˙ M ⋆ (M ⊙ yr − ) = 1 . × − L IR (L ⊙ )(Kennicutt 1998), with an averaging time of 10 to 100 Myr. This number mayvary by a factor of at least 2 depending on the star formation rate and age of astarburst (see Krumholz & Tan 2007).How does L IR correlate with various tracers of gas? If CO is used to trace themolecular gas, the relation is strongly non-linear. For CO, the “ ǫ ” increases by afactor of 100 as L IR rises from 10 to 10 L ⊙ (Solomon & Vanden Bout 2005).Even higher “ ǫ ” may be observed in high-z submillimeter galaxies (Greve et al.2005).If the L IR versus L Mol plot is made using HCN J = 1 −
0, instead ofCO, the correlation is better, the scatter is less, and the relation is linear (Gao & Solomon 2004a, Gao & Solomon 2004b). In this case, the “ ǫ ” is con-stant over more than 3 orders of magnitude in L Mol . The HCN line is sensitiveto relatively dense gas, which reminds us that it was only the dense moleculargas that is involved in star formation in well-studied local molecular clouds.In order to compare directly the situation in local clouds to that in starburstgalaxies, Wu et al. (2005) surveyed the HCN J = 1 − tar Formation in Molecular Clouds? Figure 1. Correlations between the distance-independent ratio L IR / L Mol vs. L IR for HCN J = 1 − J = 3 −
2. The squares are HCN J = 1 − L IR / L HCN ratio for galaxies; the vertical dashed line in the top plot showsthe cutoff at L IR = 10 . L ⊙ . These two lines are also shown in the bottomplot to indicate the relative shifts of L IR / L Mol between HCN J = 1 − J = 3 − The results showed that, above a threshold in L Mol or L IR , the Galactic clumpsfit a linear relation between L IR and L Mol , essentially identical to that of thestarburst galaxies. Above the threshold in L IR of about 10 . L ⊙ , the “efficiency,” L IR / L Mol , is very similar in the clumps to that in starbursts (Fig. 1). Belowthe threshold, L IR / L Mol drops rapidly with decreasing L IR . While data on theHCN J = 3 − L IR / L Mol (Fig. 1). A higher ratio is notsurprising because the HCN J = 3 − + have been used in studies of dense gas in our Galaxy. Graci´a-Carpio et al.(2006) recently suggested that HCO + could be a better tracer in galaxies, butPapadopoulos (2007) came to the opposite conclusion and noted the need formore observations of higher J transitions to constrain the conditions in the dense Evans, N. gas. A recent multitransition study of CS, HCN, and HCO + in two local ULIRGs(Greve et al. 2006) found many similarities to the properties of dense clumps inthe Galaxy. They concluded that, for the transitions they studied, HCO + , HCN,and CS probe progressively denser gas.
5. An Emerging Picture
The comparisons in the last section suggest that local studies of massive starformation can indeed provide insights into starbursts. Qualitatively, a modeststarburst can happen if a galaxy has a lot of molecular gas, with some fractionof it being dense. For an extreme starburst, a large fraction of the moleculargas must be dense. At the extreme, the entire ISM might look like the dense,cluster-forming clumps in our Galaxy.Quantitatively, we offer some “Schmidt laws” (Wu et al. (2005):˙ M ⋆ (M ⊙ yr − ) = 1 . × − L HCN (K km s − pc )˙ M ⋆ (M ⊙ yr − ) = 1 . × − M ( dense )(M ⊙ )where L HCN is the monochromatic line luminosity of the HCN J = 1 − M ⋆ = 2 . × − L IR and M ( dense )(M ⊙ ) = 7 L HCN (K km s − pc − ) (Wu et al. 2005). While these arenot yet of practical use, CARMA and
ALMA will be supplying much more ob-servational data on the lines in the coming years. In the meantime, we shouldtry to understand the relationship between these linear relations for dense gasand the non-linear relations for less dense gas.First, we should ask why L IR / L HCN is constant from L IR = 10 . to 10 L ⊙ , but drops sharply for lower L IR . At first glance, the constancy is quitepuzzling for Galactic clumps even if the star formation rate is linear with theamount of dense gas because one would expect the mass of the most massivestar to increase with the number of stars formed and the stellar luminosity is anon-linear function of the stellar mass. Thus, one might expect L IR to increasenon-linearly with M ( dense ). In fact, it does exactly that below the thresholdof L IR ∼ . L ⊙ . This is a clue. Wu et al. (2005) proposed that there is a“basic unit” of massive clustered star formation. For clumps below the massof the basic unit, the IMF is not fully sampled and L IR increases non-linearlywith M ( dense ). Once the mass exceeds the threshold, the IMF is fairly wellsampled. Further increases in mass produce more stars but no further change in L IR / M ( dense ). In this picture, the difference between star formation in Galacticmolecular clouds, normal galaxies, starbursts, and ULIRGS is simply how manysuch basic units (or how much dense gas) they contain. To be concrete, a L IR of 10 L ⊙ corresponds to a stellar mass of about 30 to 40 L ⊙ . The basic unitcontains 300 to 1000 M ⊙ of dense ( n > cm − ) gas. This picture also explainswhy the scatter in L IR / L HCN is greater in the Galactic clumps than in galaxies:the most massive star formed will be subject to stochastic fluctuations, whichcan produce order of magnitude fluctuations in the ratio. These tend to averageout for a whole galaxy. tar Formation in Molecular Clouds? L IR / L CO increases with L IR . While CO traces theoverall mass in Galactic clouds, it fails completely to trace the mass in denseclumps and cores. This failure is not surprising as CO is optically thick andthermalized easily. CO does not trace the gas that is relevant to star formation.Roughly speaking L HCN / L CO provides an estimate of the fraction of dense gas,as long as that fraction is not too large. Indeed, this ratio increases with L IR ,as expected in this picture (Gao & Solomon 2004a).
6. Future Directions
Further studies are needed in both the Galactic and extragalactic context. Sys-tematic, unbiased surveys of the Galactic plane for dense clumps will remove thebiases in the samples used so far and provide a much larger data set. Already theBolocam Galactic Plane Survey has found thousands of clumps (Williams et al.2007) and deeper surveys are on the way. With large samples in different en-vironments, we can begin to understand the dependence of the relations onchemistry, metallicity, environment, etc. Extragalactic studies should test therelations at lower L IR , aided by the tremendous sensitivity of ALMA . Furtherstudies of the very luminous end will also be important, and higher J lines ofdense gas tracers can be studied in many more sources.We also need to understand the non-linear Kennicutt relations and theirrelationship to the linear relations for dense gas. Theories need to explain both relations. It is important to realize that the gas surface density, which appearsin the Kennicutt relations, is two steps removed from the actual star formingentities: dense clumps and cores. We need to understand how the large-scalesurface density controls the formation of molecular clouds and what controlsthe formation of dense clumps and cores within those clouds. The first stepmay be best studied with high resolution observations of other galaxies and de-tailed comparison to simulations with sufficient resolution to separate individualmolecular clouds. The second step, from molecular clouds to dense clumps andcores, will be hard to study in other galaxies because of resolution issues, thoughinsights may be available from studies of other galaxies to see how L HCN / L CO ,for example, depends on conditions. For the most part, though, we need tostudy the formation of dense cores from molecular clouds with more unbiasedand complete studies of molecular clouds in our Galaxy.I will close by thanking the organizers for providing a forum that allowedsome of us touching different parts of the elephant to struggle at least toward acommon language. Acknowledgments.
I am grateful to Jingwen Wu, whose work underliesthe latter part of this paper. Many of my c2d colleagues have provided informa-tion in advance of publication, most notably Melissa Enoch. Leo Blitz providedguidance on local surface densities of gas. This work has been supported byNSF Grants AST-0307250 and AST-0607793. Additional support came fromNASA Origins grants NNG04GG24G and NNX07AJ72G. The c2d project waspart of the
Spitzer
Legacy Science Program, with support provided by NASAthrough contracts 1224608, 1230779, and 1230782 issued by the Jet PropulsionLaboratory, California Institute of Technology, under NASA contract 1407.0
Evans, N.
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